The Chi-Square Test (χ²): When to Use It, How to Run It in SPSS and How to Report It
Chi-square for independence and goodness of fit - when it fits, the expected-count assumption, reading the Crosstabs output, effect size (Cramér's V) and APA reporting, with a full example.
Part of the series: Statistical Analysis for a Seminar Paper or Thesis: The Complete Guide
Chi-square is the test for categorical variables: when both the outcome and the predictor are categories, not scores. For example: is gender (male/female) related to the study track chosen (social sciences / sciences / humanities)?
Two kinds
| Kind | Question | Example |
|---|---|---|
| Chi-square test of independence | Are two categorical variables related? | gender × study track |
| Goodness-of-fit chi-square | Does one variable's distribution differ from an expected one? | are students split evenly across three tracks? |
Most seminar papers need the first.
Assumptions
- Independent observations: each participant counted once, in one cell.
- Expected counts: at least 5 in each cell (or no more than 20% of cells below 5). SPSS prints this under the table: "0 cells (0.0%) have expected count less than 5".
If this fails in a 2×2 table, use Fisher's exact test, printed in the same SPSS table. In bigger tables, merge small categories.
In SPSS
Analyze → Descriptive Statistics → Crosstabs; one variable in Rows, the other in Columns. - Statistics: tick Chi-square and Phi and Cramer's V. - Cells: tick Observed, Expected and Row or Column percentages - without percentages you can't read the direction.
Reading the output
- Crosstabulation table: counts and percentages - this is where you see where the difference is.
- Chi-Square Tests: read the Pearson Chi-Square row - value, df and Asymptotic Significance. In a 2×2 with small cells, use the Fisher's Exact Test row.
- Symmetric Measures: Cramér's V (or Phi for 2×2) - the effect size. Roughly 0.1 small, 0.3 medium, 0.5 large for df = 1 (lower thresholds with more categories).
Reporting in APA
"Gender was significantly related to the choice of study track, χ²(2, N = 180) = 9.84, p = .007, V = .23. A higher share of women chose the social sciences (58%) than men (37%), with the opposite pattern in the sciences."
Both df and N go in the parentheses, and significance alone isn't enough: describe the percentages so the reader sees the direction.
Common mistakes
- Using chi-square on continuous scores (e.g. cutting age into groups for no reason) - it throws information away. For a score across groups use a t-test or ANOVA.
- Counting the same participant twice (e.g. multiple-answer questions).
- Ignoring the expected-count warning.
- Reporting χ² and p without percentages or direction.
FAQ
A categorical variable measured twice (before/after)? Not ordinary chi-square - use McNemar's test.
2×2 table: Pearson or Continuity Correction? Pearson is the usual report; Yates' correction is overly conservative. With small cells, Fisher.
Where does it fit? Step 4 of 7 - Statistical analysis for a seminar paper: the complete guide; choosing the test: How to choose a statistical test. Not sure your data fits? Tell us.
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